Caesar ofers a centurion the following bet: if a six-sided die is thrown and an

Question

Caesar ofers a centurion the following bet: if a six-sided die is thrown and an even value comes up, he will receive a ration of salt that is twice as large as his usual ration. If an odd value comes up, he will receive no ration of salt. a. Suppose we set V(no ration) = 0 and V(winning ration) = 1. What is the expected value of taking the bet? b. he centurion declines the bet that Caesar ofers. But he would be willing to take the bet, if Caesar changed the rules, so that he received a double-ration if an even number or a ive comes up. What is the value of the centurion’s usual ration?
Caesar ofers a centurion the following bet: if a six-sided die is thrown and an even value comes up, he will receive a ration of salt that is twice as large as his usual ration. If an odd value comes up, he will receive no ration of salt. a. Suppose we set V(no ration) = 0 and V(winning ration) = 1. What is the expected value of taking the bet? b. he centurion declines the bet that Caesar ofers. But he would be willing to take the bet, if Caesar changed the rules, so that he received a double-ration if an even number or a ive comes up. What is the value of the centurion’s usual ration?
Caesar ofers a centurion the following bet: if a six-sided die is thrown and an even value comes up, he will receive a ration of salt that is twice as large as his usual ration. If an odd value comes up, he will receive no ration of salt. a. Suppose we set V(no ration) = 0 and V(winning ration) = 1. What is the expected value of taking the bet? b. he centurion declines the bet that Caesar ofers. But he would be willing to take the bet, if Caesar changed the rules, so that he received a double-ration if an even number or a ive comes up. What is the value of the centurion’s usual ration?

Explanation / Answer

Ans(a):

Then expected value= 0*(1/6)+ 1*(1/6)+ 0*(1/6)+ 1*(1/6)+ 0*(1/6)+ 1*(1/6) = 1/6+ 1/6+ 1/6 = 3/6= 1/2

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Ans(b):

Then expected value= 0*(1/6)+ 1*(1/6)+ 0*(1/6)+ 1*(1/6)+ 1*(1/6)+ 1*(1/6) = 1/6+ 1/6+ 1/6 + 1/6 = 4/6= 2/3

so there is 2/3rd probability that centurian will get two times ration.

possible output 1 2 3 4 5 6 probabability of each output 1/6 1/6 1/6 1/6 1/6 1/6 V 0 1 0 1 0 1

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